# Publications

## Analysing surveys of our Galaxy - II. Determining the potential

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 433 (2013) 1411-1424

PJ McMillan, JJ Binney

## Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

ArXiv (2012)

NF Loureiro, AA Schekochihin, DA Uzdensky

A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {\bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids ($k_{\rm max}\Lsheet \sim S^{3/8}$, where $k_{\rm max}$ is the wave-number of fastest growing mode, $S=\Lsheet V_A/\eta$ is the Lundquist number, $\Lsheet$ is the length of the sheet, $V_A$ is the Alfv\'en speed and $\eta$ is the plasma resistivity), which grows super-Alfv\'enically fast ($\gmax\tau_A\sim S^{1/4}$, where $\gmax$ is the maximum growth rate, and $\tau_A=\Lsheet/V_A$). For typical background profiles, the growth rate and the wave-number are found to {\it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfv\'en speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, $\gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}$. The effect of viscosity ($\nu$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm=\nu/\eta$, it is found that $\gmax\sim S^{1/4}Pm^{-5/8}$ and $k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}$, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pm\gg1$ regime is $\Scrit\sim 10^4Pm^{1/2}$. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.

## Numerical modeling of the sensitivity of x-ray driven implosions to low-mode flux asymmetries

Physical Review Letters 110 (2013)

RHH Scott, PA Norreys, DS Clark, DK Bradley, DA Callahan, MJ Edwards, SW Haan, OS Jones, BK Spears, MM Marinak, RPJ Town, LJ Suter

The sensitivity of inertial confinement fusion implosions, of the type performed on the National Ignition Facility (NIF), to low-mode flux asymmetries is investigated numerically. It is shown that large-amplitude, low-order mode shapes (Legendre polynomial P), resulting from low-order flux asymmetries, cause spatial variations in capsule and fuel momentum that prevent the deuterium and tritium (DT) "ice" layer from being decelerated uniformly by the hot spot pressure. This reduces the transfer of implosion kinetic energy to internal energy of the central hot spot, thus reducing the neutron yield. Furthermore, synthetic gated x-ray images of the hot spot self-emission indicate that P shapes may be unquantifiable for DT layered capsules. Instead the positive P asymmetry "aliases" itself as an oblate P in the x-ray images. Correction of this apparent P distortion can further distort the implosion while creating a round x-ray image. Long wavelength asymmetries may be playing a significant role in the observed yield reduction of NIF DT implosions relative to detailed postshot two-dimensional simulations. © 2013 American Physical Society.

## Linear structures in the core of the Coma cluster of galaxies

Science 341 (2013) 1365-1368

JS Sanders, AC Fabian, SA Walker, E Churazov, AA Schekochihin, A Simionescu, N Werner

The hot x-ray-emitting plasma in galaxy clusters is predicted to have turbulent motion, which can contribute around 10% of the cluster's central energy density. We report deep Chandra X-ray Observatory observations of the Coma cluster core, showing the presence of quasi-linear high-density arms spanning 150 kiloparsecs, consisting of low-entropy material that was probably stripped from merging subclusters. Two appear to be connected with a subgroup of galaxies at a 650-kiloparsec radius that is merging into the cluster, implying coherence over several hundred million years. Such a long lifetime implies that strong isotropic turbulence and conduction are suppressed in the core, despite the unrelaxed state of the cluster. Magnetic fields are presumably responsible. The structures seen in Coma present insight into the past billion years of subcluster merger activity.

## Satellite Survival in Highly Resolved Milky Way Class Halos

ArXiv (2012)

S Geen, A Slyz, J Devriendt

Surprisingly little is known about the origin and evolution of the Milky Way's satellite galaxy companions. UV photoionisation, supernova feedback and interactions with the larger host halo are all thought to play a role in shaping the population of satellites that we observe today, but there is still no consensus as to which of these effects, if any, dominates. In this paper, we revisit the issue by re-simulating a Milky Way class dark matter (DM) halo with unprecedented resolution. Our set of cosmological hydrodynamic Adaptive Mesh Refinement (AMR) simulations, called the Nut suite, allows us to investigate the effect of supernova feedback and UV photoionisation at high redshift with sub-parsec resolution. We subsequently follow the effect of interactions with the Milky Way-like halo using a lower spatial resolution (50pc) version of the simulation down to z=0. This latter produces a population of simulated satellites that we compare to the observed satellites of the Milky Way and M31. We find that supernova feedback reduces star formation in the least massive satellites but enhances it in the more massive ones. Photoionisation appears to play a very minor role in suppressing star and galaxy formation in all progenitors of satellite halos. By far the largest effect on the satellite population is found to be the mass of the host and whether gas cooling is included in the simulation or not. Indeed, inclusion of gas cooling dramatically reduces the number of satellites captured at high redshift which survive down to z=0.

## Present status of fast ignition realization experiment and inertial fusion energy development

Nuclear Fusion 53 (2013)

H Azechi, S Shiraga, S Fujioka, H Nagatomo, T Jitsuno, J Kawanaka, N Miyanaga, M Murakami, M Nakai, T Nakazato, K Nishihara, H Nishimura, T Norimatsu, Y Sakawa, N Sarukura, K Shigemori, T Shimizu, K Tsubakimoto, Y Fujimoto, K Mima, T Johzaki, M Key, R Kodama, K Tanaka, M Koga, K Kondo, T Nakamura, K Nagai, H Nakamura, Y Nakao, P Norreys, T Ozaki, H Sakagami, A Iwamoto, J Pasley, A Sunahara, T Taguchi, H Homma

One of the most advanced fast ignition programmes is the fast ignition realization experiment (FIREX). The goal of its first phase is to demonstrate ignition temperature of 5 keV, followed by the second phase to demonstrate ignition-and-burn. The second series experiment of FIREX-I, from late 2010 to early 2011, has demonstrated a high (>10%) coupling efficiency from laser to thermal energy of the compressed core, suggesting that the ignition temperature can be achieved at laser energy below 10 kJ. Further improvement of the coupling efficiency is expected by introducing laser-driven magnetic fields. © 2013 IAEA, Vienna.

## Magnetic field generation by Biermann battery and Weibel instability in laboratory shock waves

EAS Publications Series 58 (2012) 23-26

G Gregori, B Reville, F Miniati, RP Drake

Magnetic field generation in the Universe is still an open problem. Possible mechanisms involve the Weibel instability, due to anisotropic phase-space distributions, as well as the Biermann battery, due to misaligned density and temperature gradients. These mechanisms can be reproduced in scaled laboratory experiments. In this contribution we estimate the relative importance of these two processes and explore the laser-energy requirements for producing Weibel dominated shocks. © The Author(s) 2013.

## The wobbly Galaxy: Kinematics north and south with RAVE red-clump giants

Monthly Notices of the Royal Astronomical Society 436 (2013) 101-121

MEK Williams, M Steinmetz, H Enke, I Minchev, RS de Jong, A Siviero, J Binney, A Siebert, B Famaey, O Bienaymé, C Boeche, EK Grebel, KC Freeman, J Bland-Hawthorn, S Sharma, BK Gibson, GF Gilmore, G Kordopatis, A Helmi, U Munari, JF Navarro, QA Parker, W Reid, GM Seabroke, FG Watson, RFG Wyse, T Zwitter

TheRAdialVelocity Experiment survey, combined with proper motions and distance estimates, can be used to study in detail stellar kinematics in the extended solar neighbourhood (solar suburb). Using 72 365 red-clump stars, we examine the mean velocity components in 3D between 6 < R < 10 kpc and -2 < Z < 2 kpc, concentrating on north-south differences. Simple parametric fits to the (R, Z) trends for V and the velocity dispersions are presented. We confirm the recently discovered gradient in mean Galactocentric radial velocity, V, finding that the gradient is marked below the plane (δ(V)/δR=-8 kms kpc for Z<0, vanishing to zero above the plane), with a Z gradient thus also present. The vertical velocity, V, also shows clear, large-amplitude (|V| = 17 km s) structure, with indications of a rarefaction- compression pattern, suggestive of wave-like behaviour. We perform a rigorous error analysis, tracing sources of both systematic and random errors. We confirm the north-south differences in V and V along the line of sight, with the V estimated independent of the proper motions. The complex three-dimensional structure of velocity space presents challenges for future modelling of the Galactic disc, with the Galactic bar, spiral arms and excitation of wave-like structures all probably playing a role. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

## Dynamical models and Galaxy surveys

ArXiv (2013)

J Binney, JL Sanders

Equilibrium dynamical models are essential tools for extracting science from surveys of our Galaxy. We show how models can be tested with data from a survey before the survey's selection function has been determined. We illustrate the application of this method by presenting some results for the RAVE survey. We extend our published analytic distribution functions to include chemistry and fit the chosen functional form to a combination of the Geneva--Copenhagen survey (GCS) and a sample of G-dwarfs observed at z~1.75 kpc by the SEGUE survey. By including solid dynamics we are able to predict the contribution that the thick disc/halo stars surveyed by SEGUE should make to the GCS survey. We show that the measured [Fe/H] distribution from the GCS includes many fewer stars at [Fe/H]<-0.6 than are predicted. The problem is more likely to lie in discordant abundance scales than with incorrect dynamics.

## Measuring fast electron spectra and laser absorption in relativistic laser-solid interactions using differential bremsstrahlung photon detectors.

Rev Sci Instrum 84 (2013) 083505-

RH Scott, EL Clark, F Pérez, MJ Streeter, JR Davies, HP Schlenvoigt, JJ Santos, S Hulin, KL Lancaster, SD Baton, SJ Rose, PA Norreys

A photon detector suitable for the measurement of bremsstrahlung spectra generated in relativistically intense laser-solid interactions is described. The Monte Carlo techniques used to extract the fast electron spectrum and laser energy absorbed into forward-going fast electrons are detailed. A relativistically intense laser-solid experiment using frequency doubled laser light is used to demonstrate the effective operation of the detector. The experimental data were interpreted using the 3-spatial-dimension Monte Carlo code MCNPX [D. Pelowitz, MCNPX User's Manual Version 2.6.0, Los Alamos National Laboratory, 2008], and the fast electron temperature found to be 125 keV.

## X-ray scattering by many-particle systems

New Journal of Physics 15 (2013)

BJB Crowley, G Gregori

This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio ω α /ω β of the scattered (α) to primary (β) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In Compton scattering, the frequency change is generally understood to be due to the recoil of the particle as a result of energy and momentum conservation in the photon-electron system. In this case, the Klein-Nishina formula gives the redistribution factor as . In the case of scattering by a many-particle system, however, the frequency and momentum changes are no longer directly interdependent but depend also upon the properties of the medium, which are encoded in the dynamic structure factor. We show that the redistribution factor explicit in the quantum cross-section (that seen by a photon) is ω α /ω β, which is not squared. Formulae for the many-body cross-section given in the literature, in which the factor is squared, can often be attributed to a different (classical) definition of the cross-section, though not all authors are explicit about which definition they are using. What is shown not to be true is that the structure factor simply gives the ratio of the many-electron to one-electron differential cross-sections, as is sometimes supposed. Mixing up the cross-section definitions can lead to errors when describing x-ray scattering. We illustrate the nature of the discrepancy by deriving the energy-integrated angular distributions, with first-order relativistic corrections, for classical and quantum scattering measurements, as well as the radiative opacity for photon diffusion in a Thomson-scattering medium, which is generally considered to be governed by quantum processes. © IOP Publishing and Deutsche Physikalische Gesellschaft.

## Swirling around filaments: are large-scale structure vortices spinning up dark halos?

ArXiv (2013)

C Laigle, C Pichon, S Codis, Y Dubois, DL Borgne, D Pogosyan, J Devriendt, S Peirani, S Prunet, S Rouberol, A Slyz, T Sousbie

The kinematic analysis of dark matter and hydrodynamical simulations suggests that the vorticity in large-scale structure is mostly confined to, and predominantly aligned with their filaments, with an excess of probability of 20 per cent to have the angle between vorticity and filaments direction lower than 60 degrees relative to random orientations. The cross sections of these filaments are typically partitioned into four quadrants with opposite vorticity sign, arising from multiple flows, originating from neighbouring walls. The spins of halos embedded within these filaments are consistently aligned with this vorticity for any halo mass, with a stronger alignment for the most massive structures up to an excess of probability of 165 per cent. On large scales, adiabatic/cooling hydrodynamical simulations display the same vorticity in the gas as in the dark matter. The global geometry of the flow within the cosmic web is therefore qualitatively consistent with a spin acquisition for smaller halos induced by this large-scale coherence, as argued in Codis et al. (2012). In effect, secondary anisotropic infall (originating from the vortex-rich filament within which these lower-mass halos form) dominates the angular momentum budget of these halos. The transition mass from alignment to orthogonality is related to the size of a given multi-flow region with a given polarity. This transition may be reconciled with the standard tidal torque theory if the latter is augmented so as to account for the larger scale anisotropic environment of walls and filaments.

## Dense electron-positron plasmas and bursts of gamma-rays from laser-generated quantum electrodynamic plasmas

Physics of Plasmas 20 (2013)

CP Ridgers, AR Bell, CS Brady, K Bennett, TD Arber, R Duclous, JG Kirk

In simulations of a 12.5 PW laser (focussed intensity I = 4 × 10 23 Wcm - 2) striking a solid aluminum target, 10% of the laser energy is converted to gamma-rays. A dense electron-positron plasma is generated with a maximum density of 10 26 m - 3, seven orders of magnitude denser than pure e e plasmas generated with 1PW lasers. When the laser power is increased to 320 PW (I = 10 25 Wcm - 2), 40% of the laser energy is converted to gamma-ray photons and 10% to electron-positron pairs. In both cases, there is strong feedback between the QED emission processes and the plasma physics, the defining feature of the new "QED-plasma" regime reached in these interactions. © 2013 AIP Publishing LLC.

## Cosmic-ray acceleration and escape from supernova remnants

Monthly Notices of the Royal Astronomical Society 431 (2013) 415-429

AR Bell, KM Schure, B Reville, G Giacinti

Galactic cosmic-ray (CR) acceleration to the knee in the spectrum at a few PeV is only possible if the magnetic field ahead of a supernova remnant (SNR) shock is strongly amplified by CRs escaping the SNR. A model formulated in terms of the electric charge carried by escaping CRs predicts the maximum CR energy and the energy spectrum of CRs released into the surrounding medium. We find that historical SNRs such as Cas A, Tycho and Kepler may be expanding too slowly to accelerate CRs to the knee at the present time. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

## Powering of cool filaments in cluster cores by buoyant bubbles - I. Qualitative model

Monthly Notices of the Royal Astronomical Society 436 (2013) 526-530

E Churazov, M Ruszkowski, A Schekochihin

Cool-core clusters (e.g. Perseus or M87) often possess a network of bright gaseous filaments, observed in radio, infrared, optical and X-ray bands. We propose that these filaments are powered by the reconnection of the magnetic field in the wakes of buoyant bubbles. Active galactic nucleus (AGN)-inflated bubbles of relativistic plasma rise buoyantly in the cluster atmosphere, stretching and amplifying the field in the wake to values of β = 8πP/B ~ 1. The field lines in thewake have opposite directions and are forced together as the bubble motion stretches the filament. This setup bears strong similarity to the coronal loops on the Sun or to the Earth's magnetotail. The reconnection process naturally explains both the required level of local dissipation rate in filaments and the overall luminosity of filaments. The original source of power for the filaments is the potential energy of buoyant bubbles, inflated by the central AGN. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

## Surface waves and electron acceleration from high-power, kilojoule-class laser interactions with underdense plasma

New Journal of Physics 15 (2013)

L Willingale, AGR Thomas, A Maksimchuk, C Zulick, K Krushelnick, PM Nilson, RS Craxton, TC Sangster, C Stoeckl, H Chen, J Cobble, PA Norreys, RHH Scott

Experiments were performed on the Omega EP laser facility to study laser pulse propagation, channeling phenomena and electron acceleration from high-intensity, high-power laser interactions with underdense plasma. A CH plasma plume was used as the underdense target and the interaction of the laser pulse channeling through the plasma was imaged using proton radiography. High-energy electron spectra were measured for different experimental laser parameters. Structures observed along the channel walls are interpreted as having developed from surface waves, which are likely to serve as an injection mechanism of electrons into the cavitated channel for acceleration via direct laser acceleration mechanisms. Two-dimensional particle-in-cell simulations give good agreement with these channeling and electron acceleration phenomena. © IOP Publishing and Deutsche Physikalische Gesellschaft.

## Cosmic ray acceleration in young supernova remnants

Monthly Notices of the Royal Astronomical Society 435 (2013) 1174-1185

KM Schure, AR Bell

We investigate the appearance of magnetic field amplification resulting from a cosmic ray escape current in the context of supernova remnant shock waves. The current is inversely proportional to the maximum energy of cosmic rays, and is a strong function of the shock velocity. Depending on the evolution of the shock wave, which is drastically different for different circumstellar environments, the maximum energy of cosmic rays as required to generate enough current to trigger the non-resonant hybrid instability that confines the cosmic rays follows a different evolution and reaches different values.We find that the best candidates to accelerate cosmic rays to ~ few PeV energies are young remnants in a dense environment, such as a red supergiant wind, as may be applicable to Cassiopeia A. We also find that for a typical background magnetic field strength of 5 μG the instability is quenched in about 1000 years, making SN1006 just at the border of candidates for cosmic ray acceleration to high energies. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

## Magnetic field amplification by cosmic rays in supernova remnants

370 YEARS OF ASTRONOMY IN UTRECHT 470 (2013) 209-214

KM Schure, AR Bell

## Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas

Physics of Plasmas 20 (2013)

KA Humphrey, DC Speirs, R Bingham, RMGM Trines, P Norreys, F Fiuza, RA Cairns, LO Silva

We report on particle in cell simulations of energy transfer between a laser pump beam and a counter-propagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed pre-pulse produced. © 2013 AIP Publishing LLC.

## Correlations at large scales and the onset of turbulence in the fast solar WIND

Astrophysical Journal 778 (2013)

RT Wicks, DA Roberts, A Mallet, AA Schekochihin, TS Horbury, CHK Chen

We show that the scaling of structure functions of magnetic and velocity fields in a mostly highly Alfvénic fast solar wind stream depends strongly on the joint distribution of the dimensionless measures of cross helicity and residual energy. Already at very low frequencies, fluctuations that are both more balanced (cross helicity ∼0) and equipartitioned (residual energy ∼0) have steep structure functions reminiscent of "turbulent" scalings usually associated with the inertial range. Fluctuations that are magnetically dominated (residual energy ∼-1), and so have closely anti-aligned Elsasser-field vectors, or are imbalanced (cross helicity ∼1), and so have closely aligned magnetic and velocity vectors, have wide "1/f" ranges typical of fast solar wind. We conclude that the strength of nonlinear interactions of individual fluctuations within a stream, diagnosed by the degree of correlation in direction and magnitude of magnetic and velocity fluctuations, determines the extent of the 1/f region observed, and thus the onset scale for the turbulent cascade. © 2013. The American Astronomical Society. All rights reserved.